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adoni [48]
3 years ago
14

Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.

Mathematics
1 answer:
yanalaym [24]3 years ago
4 0

Answer;

They will be 0.5x miles away from each other

Explanation;

Since the dog runs twice the speed of the cat

Its speed will be 2 * x = 2x mph

Now we want to know how far they will be from each other after 30 minutes

Kindly note that 30 minutes is 1/2 hour

Mathematically;

distance = speed * time

Distance of cat = x * 1/2 = 0.5x miles

Distance of dog = 2x * 0.5 = x miles

The dog is x - 0.5x miles = 0.5x miles away from the cat

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3 years ago
In Exercises 5-7, find all the exact t-values for which the given statement is true,
bearhunter [10]

Answer:  See Below

<u>Step-by-step explanation:</u>

NOTE: You need the Unit Circle to answer these (attached)

5) cos (t) = 1

Where on the Unit Circle does cos = 1?

Answer: at 0π (0°) and all rotations of 2π (360°)

In radians:     t = 0π + 2πn

In degrees:   t = 0° + 360n

******************************************************************************

6)\quad sin (t) = \dfrac{1}{2}

Where on the Unit Circle does   sin = \dfrac{1}{2}

<em>Hint: sin is only positive in Quadrants I and II</em>

\text{Answer: at}\  \dfrac{\pi}{6}\ (30^o)\ \text{and at}\ \dfrac{5\pi}{6}\ (150^o)\ \text{and all rotations of}\ 2\pi \ (360^o)

\text{In radians:}\ t = \dfrac{\pi}{6} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{6} + 2\pi n

In degrees:    t = 30° + 360n  and  150° + 360n

******************************************************************************

7)\quad tan (t) = -\sqrt3

Where on the Unit Circle does    \dfrac{sin}{cos} = \dfrac{-\sqrt3}{1}\ or\ \dfrac{\sqrt3}{-1}\quad \rightarrow \quad (1,-\sqrt3)\ or\ (-1, \sqrt3)

<em>Hint: sin and cos are only opposite signs in Quadrants II and IV</em>

\text{Answer: at}\  \dfrac{2\pi}{3}\ (120^o)\ \text{and at}\ \dfrac{5\pi}{3}\ (300^o)\ \text{and all rotations of}\ 2\pi \ (360^o)

\text{In radians:}\ t = \dfrac{2\pi}{3} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{3} + 2\pi n

In degrees:    t = 120° + 360n  and  300° + 360n

4 0
3 years ago
Kasey and Jordan are counting calories while eating lunch in the school cafeteria. In one week, Kasey had
malfutka [58]

Answer:

Jordan got 222 calories from pizza

Step-by-step explanation:

Given:

slices of pizza ate by Kasey =10

cups of fruit salad by Kasey=  5

slices of pizza ate by Jordan = 6

cups of fruit salad by Jordan=  7

Kasey's calorie  count = 3070

Jordan calorie  count = 2522

To Find:

calories Jordan got from pizza =?

Solution:

Let the calorie of one slice of pizza be  x

and the  calorie of one cup of fruit salad be  y

According to the question, the equation that represents the Kasey's Scenario is

10x + 5y = 3070-------------------------------------(1)

Similarly the equation that represents the Jordan Scenario is

6x + 7y = 2522--------------------------------------(2)

multiply eq(1) by 6 we get

60x + 30y = 18420---------------------------------(3)

multiply eq(2) by 10 we get,

60x + 70y = 25220----------------------------------(4)

Subtracting eq (3) from (4) we get

  60x + 70y = 25220

  60x + 30y = 18420

  (-)        (-)        (-)

-----------------------------------

 0x + 40y = 6800

---------------------------------

=>40 y = 6800

=>y = \frac{6800}{40}

=> y = 170

So calorie of one cup fruit salad is = 170 calories

substituting the y values in eq 1 we get

10x + 5(170) = 3070

10x + 850 = 3070

10x = 3070 - 850

10x = 2220

x = \frac{2220}{10}

x= 222

So calorie of one pizza slice = 222 calories

Now we know that  Jordan ate 6 slices of pizza

calories  Jordan get from pizza = number of pizza he ate  X calore per pizza slice

=> 6 x 222

=>1332 calories

6 0
3 years ago
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